Question

A hole with a diameter of 3.5cm is drilled through a square metal nut of a thickness 4cm and length 6cm. What is the surface area?

Answer 1

Answer:

168.75 square cm.

Step-by-step explanation:

The hole creates a cylinder in the Square block.

Since the piece is drilled out, it creates new surface in between the square block. That is equal to lateral surface area of the cylinder.

Total surface area of cylinder = 2 π r^2 + 2 π r h

but 2πrh will remain inside the square block.

2πr^2 will go out of square block.

So new surface area on the square block = surface area of square - 2πr^2 + 2πrh

r = 3.5/2 cm

h = 4 cm.

a = 6 cm (side of square)

New surface area = a*a*h - 2πr^2 + 2πrh

= 6*6*4 - 2*22*3.5*3.5/(2*2*7) + 2*22*3.5*4/(2*7)

= 144 - 77/4 + 44

= 168.75 square cm.